A skepticism on the concept of quantum state related to quantum field theory on curved spacetime

TL;DR

The paper questions the physical reality of quantum states in quantum field theory on curved spacetime, arguing that the lack of a distinguished Hilbert space undermines their physical interpretation.

Contribution

It presents a skeptical argument against the physical reality of quantum states in algebraic QFT on curved spacetime, challenging pragmatic realism in this context.

Findings

Algebraic QFTCS leads to skepticism about quantum state reality.

In QFTCS, no distinguished Hilbert space makes physical states indistinguishable.

Quantum states are argued to be dispensable in non-relativistic and relativistic QFT.

Abstract

Some skeptical arguments on the physical reality of quantum states are given. First, I argue that the algebraic formalism of quantum field theory in curved spacetime (algebraic QFTCS, AQFTCS) leads to such a skepticism. Of course we have the purely mathematical notion of states on a $C^{*}$-algebra $\mathfrak{A}$, but usually in non-relativistic quantum mechanics and quantum field theory in Minkowski spacetime (QFTM), not all of them are considered to be physically real; Some of them are physically real (or realizable) states, but others are non-physical ``fictional'' states. Only the states which can be expressed as a density matrix on a fixed ``physical Hilbert space'' (the GNS representation space of $\mathfrak{A}$ w.r.t. the vacuum) are viewed to be physically real. On the other hand, in QFTCS, there is no distinguished physical Hilbert space; no distinguished vacuum state. Thus we cannot distinguish physically real states from fictional states. The second part of my argument is a counterargument to what I call ``pragmatic realism on quantum states'', which insists as follows: ``We are permitted to regard a quantum state as a physical reality, because the concept of quantum state is indispensable in quantum physics.'' I argue that the concept of quantum state is indeed dispensable in non-relativistic QM, and hence this pragmatic realist thesis is vacuous there. I give a conjecture that it is also dispensable in QFTM and QFTCS, and some preliminary considerations on it.